Retaining walls serve the important role
of holding back soil and rock,
just as dams hold back water.
The first video in this series showed that
granular materials, such as soil and rock,
generate horizontal pressures
that increase linearly with depth.
Retaining walls must resist these pressures,
and many strategies exist for doing so.
In this video, we focus on a popular,
L-shaped, cantilever design.
If you were going to use an L-shaped wall
to hold back soil and rock,
as represented by these marbles,
would you point the bottom leg
toward the marbles or away from them?
Many people would say that
the base of the “L” should face away from the marbles.
They probably realize
that it is hard to tip the wall over toward the left
if the bottom leg points in that direction.
In engineering, we call tipping like this “overturning”.
If the bottom leg points the other way around,
it is easy to make the wall overturn –
so easy, in fact, that I can do it with just a puff of air.
It looks like the case is closed.
Or is it?
Before we declare a final verdict,
let’s use the model to find out what happens
when the bottom leg points to the left,
away from the marbles.
As we add marbles,
we discover that the horizontal forces they produce
create yet another mode of failure,
namely sliding of the wall.
And this occurs
when the marbles reach a depth of 3 centimeters.
In the model, we can increase the friction
between the retaining wall and the base
by placing a rubber mat between them.
You will have to do some extra reading
if you want to find out
how they achieve this end in the real world.
As you can see, increasing the friction
allows our model wall to support
a noticeably greater depth of marbles.
But it still eventually fails by overturning,
in this case, when the depth reaches 8 centimeters.
Now, let’s turn the wall around
so its bottom leg points toward the right,
the side where the marbles will be placed.
We again use a rubber sheet to prevent sliding,
and we add some marbles.
As before, the marbles generate a horizontal force
that depends on the marble depth.
You might be surprised that this wall
can hold back 11 centimeters of marbles
before it overturns.
Can you explain why the wall
can resist a greater height of marbles
when the bottom leg points toward them?
Is there an additional force that comes into play?
Recall that granular materials generate
both horizontal and vertical pressures.
When the bottom leg is oriented away from the marbles,
overturning is resisted only
by the weight of the wall itself,
and so it overturns easily.
When the bottom leg points toward the marbles,
the vertical pressure from the marbles
helps to keep the wall upright.
The downward pressure also increases the friction
between the bottom of the wall and the ground,
thereby reducing the likelihood of sliding.
When engineers design L-shaped retaining walls,
they imagine them overturning
about the point labelled Q.
They first calculate how strongly the soil pressure
will tend to make the wall rotate about Q.
We call this tendency to tip an overturning moment,
and we label it MO.
Next, they figure out the stabilizing moment, MS,
produced by the soil pushing downward
on the horizontal leg of the wall.
Lastly, they make sure that the horizontal leg
is long enough that the stabilizing moment
is at least as large as the overturning moment.
Then the retaining wall will be stable.
You might be surprised to learn
that L-shaped walls are seldom used as dams.
The reason is that pressurized water
at the bottom of the dam
can seep under the base of the dam.
And if it does, the resulting upward water pressure
on the bottom of the dam
can generate an additional moment
and make the dam overturn.
Lots of other clever approaches can be used
to design retaining walls,
but we do not have time to discuss them here.
To learn more about how soil, water and other materials interact with structures,
we hope you will view our videos on "Dams", "Silos and Tanks", and "Tunnels and Culverts".